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Mechanical Properties Of Fluids

Question
CBSEENPH11020517

The molecules of a given mass of a gas have r.m.s. velocity of 200 m/s at 27o C and 1.0 x 105 Nm-2 pressure. When the temperature and pressure of the gas are respectively, 127o C and 0.05 x 105  Nm-2, the RMS velocity of its molecules in m/s is,

  • fraction numerator 400 over denominator square root of 3 end fraction
  • fraction numerator 100 square root of 2 over denominator 3 end fraction
  • 100 over 3
  • 100 square root of 2

Solution

A.

fraction numerator 400 over denominator square root of 3 end fraction

It is given that,
vrms = 200 m/s
T1 = 300 K
P1 = 105 N/m2 
rms velocity of gas molecules, vrms proportional to square root of straight T open square brackets straight v subscript rms space equals space square root of fraction numerator 3 RT over denominator straight m end fraction end root close square brackets
For two different cases,
space space space space space fraction numerator open parentheses straight v subscript rms close parentheses subscript 1 over denominator left parenthesis straight V subscript rms right parenthesis subscript 2 end fraction space equals square root of space T subscript 1 over T subscript 2 end root
rightwards double arrow space 200 over open parentheses v subscript r m s end subscript close parentheses subscript 2 equals space square root of 300 over 400 end root space equals space square root of 3 over 4 end root
rightwards double arrow space open parentheses v subscript r m s end subscript close parentheses subscript 2 space equals space fraction numerator 2 over denominator square root of 3 end fraction x 200
space space space space space space space space space space space space space space space space space space equals space fraction numerator 400 over denominator square root of 3 end fraction space m divided by s